The chances of a Federal Reserve interest-rate increase in 2015 are diminishing amid new signs of anemic economic activity, a disappointing development for central bank officials who have been hoping to move this year after a prolonged period of easy-money policies.

Lackluster readings on consumer spending, inflation and jobs have virtually eliminated the chances of a move this month. Already, two Fed governors expressed doubts this week about whether the timing will be right this year, and the recent trove of data hasn’t...